The conditional hazard function is seen as an indispensable tool in survival anal ysis and various other fields such as seismology , reliability , or medicine . The es timation of this function becomes an essential question in statistics . This subject must be approached in several angles ; according to the complexity of the problem posed , the hypotheses and the proposed data : the random variables are indepen dent and identically distributed ( Phenomenon found in the domain economic ) , the random variables are dependent ( Phenomenon found in the field seismology ) , or the variables are censored ( Phenomenon found in the medical field ) . Formally , suppose Y a random variable in R + associated with a lifetime . The hazard function , also called the hazard rate , survival rate , or failure , is defined at the point y as the probability instant that this life ends at the instant y . More precisely , the hazard function conditional on the explanatory random var